Explore the triangles that can be made with seven sticks of the same length.
Move four sticks so there are exactly four triangles.
Reasoning about the number of matches needed to build squares that share their sides.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?